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February 26th, 2008, 03:35 PM   #1
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real analysis?

1.
For x>-1, x not = 0, show that:
(1+x)^a > 1+ax, if a>1 or a<0,
(1+x)^a < 1+ax, if 0<a<1

2.
Prove that if F is continuous of [a,b] and differentiable on (a,b) and if F’(x) is not zero for any x strictly between a and b, then F(b) not equal to F(a)

3.
Show the approximate formula SqRt(1+x) = 1 + 1/2x - 1/8x^2 gives SqRt(1+x) with an error not greater than |x|^3 / 2, if |x| < 1/2
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